A354304 a(n) is the numerator of Sum_{k=0..n} (-1)^k / (k!)^2.

1, 0, 1, 2, 43, 403, 23213, 118483, 51997111, 1842647621, 327581799289, 8918414485643, 4670006130663971, 361730891537680087, 130890931830249779173, 427294615628884602769, 6534075316966068976316143, 885163015595247156635327497, 41526561745210509140249210357

Offset: 0

Author

Ilya Gutkovskiy, May 23 2022

Keywords

• nonn
• frac

Examples

			1, 0, 1/4, 2/9, 43/192, 403/1800, 23213/103680, 118483/529200, 51997111/232243200, 1842647621/8230118400, ...
		

Crossrefs

Cf. A001044, A053557, A061354, A073701, A091681, A103816, A120265, A143382, A354302, A354305 (denominators).

Programs

Mathematica

Table[Sum[(-1)^k/(k!)^2, {k, 0, n}], {n, 0, 18}] // Numerator
nmax = 18; CoefficientList[Series[BesselJ[0, 2 Sqrt[x]]/(1 - x), {x, 0, nmax}], x] // Numerator

Formula

Numerators of coefficients in expansion of BesselJ(0,2*sqrt(x)) / (1 - x).